Question

Identify this conic section.

9x^2 + 4y^2 = 36

line
circle
ellipse
parabola
hyperbola

Answer 1

What does this even mean??

Answer 2

it means what shape does the equation makes ?

Answer 3

Well yeah i get that but how do i go about figuring that out?

Answer 4

start like this
\(\large 9x^2+4y^2=36\)
devide by 4 and 9
\(\large \frac{x^2}{4}+\frac {y^2}{9}=1\)

so u have the formula of
\(\large \frac{x^2}{a^2}+\frac {y^2}{b^2}=1\)
and a dnt = b
so its ellipse :)

Answer 5

or if u dnt know the formula of ellipse
just drow it

Answer 6

Ok i see... What do you mean by *and a dnt = b so its ellipse :)*?

Answer 7

when a=b , then its a circle

Answer 8

Oh ok then lol how will i know what the rest look like?

Answer 9

when
\( a\neq b\) its ellipse

Answer 10

u wanna me to show u all of
line circle ellipse parabola hyperbola ?

Answer 11

You dont have to if you dont want to, but i want to be able to figure this out so that i can do it on my own. I have like 6 or 7 more of these lol

Answer 12

ok ill show u then , no problem lol :P

Answer 13

but did u got this so far ?

Answer 14

Oh yeah i am with you so far :)

Answer 15

ok
line equation :
y=mx+b
s,t m is the slope
and b is the y intersection
the equation is a line when its linear only ( means x, y cant have a power)
for example
y=x^2 not line

example of a line
y=x

Answer 16

OK :)

Answer 17

circle
u can define a circl by a point \( (x_0,y_0)\) and a radius \(r\)
circle equation :-
\(\Huge (x-x_0)^2+(y-y_0)^2=r^2 \)
for example
unit circle
\(\Huge x^2+y^2=1 \)
\(\Huge (x-0)^2+(y-0)^2=1^2 \)
so center (0,0) and r=1

Answer 18

got this ?

Answer 19

Oh yeah i know the equation of a circle so yeah i am with you so far :) I know the line and the circle so far...

Answer 20

ok !
parabola
its the sketch of quadratic equation , that one variable only in it have power of 2,
its general formula
\(\Huge y=ax^2+bx+c\)
for example
\(\Huge y=x^2\)

Answer 21

so got it so far ?

Answer 22

Yes! Ok i get the parabola i think...
One of my questions looks like that '16y = x^2' So would this be an example of a parabola then?

Answer 23

yep correct !

Answer 24

Ok good!! I am with you so far then :)

Answer 25

ok so the ellips its look like this

Answer 26

Ok so like an oval

Answer 27

yes its oval :)
its general formula
\(\Huge \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
so if u reach this formula u can draw it easily
just find \(a\) and \(b\)
and remember \(a \neq b \neq 0\)

Answer 28

so still the hyperbola right ?

Answer 29

Ok so just like my original problem! And yes the hyperbola is all that is left

Answer 30

so u got the ellips ?

Answer 31

Yeah ive got it :)

Answer 32

ok the hyperbola equation lookes like the ellips equation , but it has a negative sign
\(\Huge \frac{x^2}{a^2} \color{red}{-}\frac{y^2}{b^2}=1\)